I am one of those people who gets her nose very close to the surface of a painting. In my own visual art studies I focus on abstractions of movement with the intent of making an observer feel “moved” by what he or she is seeing on the canvas. I do so with differential geometric structures, and so it is that the subject of mathematics enters my writings and discussions about art. After having navigated many times through the unpredictable relationships that arise in the process of painting, emerging as if they are always there, waiting, like a puzzle, for me to excavate them, I can’t help but question the profundity of something as small as a painterly mark. It is so mundane, yet, as any painter knows, it does so much. Though hardly noticeable from a distance, up close, so much happens in this tiny moment. I am drawn over and over again to these gestures, in my work and in others. I can reason how they contribute compositionally to an artwork, yet something more always seems to be happening. Gestural marks are like excesses unbound by the rules which hold all the pieces together. They index a body’s movements in space, caught in an act which, when placed on a canvas, contribute to something greater than itself. This, to me, is the seductive element that begs my attention when observing works of art.
An essay by Giuseppe Longo, "The Cognitive Foundation of Mathematics: human gestures in proofs and mathematical incompleteness of formalisms," has informed me about the depth and complexity of a living being’s motions. The descriptions of gestures in this essay formulate an interwoveness of objects, movements, perceptions and contingencies that structure organic life. Longo writes that a gesture, a trajectory in space, should not be understood as a line made by a set of points, but rather a gestalt. He calls this trajectory of movement the width-less line. In this essay, Longo describes an abstraction of networked environments, organisms and processes that, when woven together, inform an organism’s perceptions and structure its movements. This “line,” an abstraction of linked networks in a field of relations, is always in flux. An organism is always moving, consciously or not.
It is through movement, some say, that our earliest ideas and intuitions begin to take shape. Gestures are imperative to thought, enabling us to create an intelligible organization of the universe, Longo says, “In this way, gesture, which begins in motor action, sets the roots of signification between the world and us, at the interface of both.” The movement of a body in space is an essential part of the cognition process. It instigates action, and action shapes our relationship to the world, stimulating thought. Moreover, Longo continues, "the cell like the amoeba (or a ... paramecium...), changes internally as well as in its relationships with the external: it moves. This is essential for life, from its action in space to cognitive phenomena since ‘motivity is the original intentionality’ [Merleau-Ponty, 1945].” In humans, as in other organisms, gestures become part of a performance that organizes our world and our relationship to it.